| Abstract: |
| Binary asteroids of nearly equal mass are rare, the fourth pair 2017 YE5 being discovered in 2017. The simplified four-body problem we propose bridges the familiar restricted three-body problem, that is traditionally used to model the motion of single asteroids, and the more complicated four-body problem. This simplified four-body problem allows the gravitational interaction of the asteroids in a binary pair of any mass ratio. We show that this simplified four-body problem inherits the 12 collinear relative equilibria of the four-body problem. We show in the limit as the masses of the binary asteroids go to zero that the positions of the relative equilibria are related to those of the restricted three-body problem. We further determine the linear stability of the collinear relative equilibria by factoring the characteristic polynomials of the associated matrices into quadratic and quartic factors. |
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